So Co-op is helpful here but it is still possible solo, Mayhem and RPG mode are your best two options so you want to look for 11 level games in the hard/player created section.
*Kill 250 Enemies, obtain 750 prestige and complete 10 levels without dying. (Your Co-op partner can die as many times as you like.)
Mayhem is much faster but brings the risk of a quick death and having to restart.
In RPG Mode there is much more enemies, but your health increases as you level up and replenishes after each stage, so a more secure method.
You can't play your own levels so someone must have created one like mentioned above, if you can't find one you may need to message a friend to make one with these settings.
Approach the exits slowly!!!! Occasionally if you run/dash into the exit walls, the game will bug out and you will just see the background. You cannot progress if this happens!
So once you've killed everything don't rush to the end.
Update: 9/06/2019 Safest to play 11 levels of one game type
. As Seitzz points out below it may not work if only the first level is Mayhem and the rest are a mixed bunch.